Causality and chronology are fundamental elements in the theory of special relativity. In this theory, the chronology is preserved and causality is respected. From a local point of view, GR has the same causal structure as special relativity, since GR space-times are locally Minkowskian. However, on a global scale, the field equations of GR do not require non-local constraints on the space-times, then interesting differences can arise. There are solutions to the GR field equations that present violation of causality in the form of Closed Timelike Curves (CTCs). As an example, the Gödel solution can be considered. This cosmological model shows that, although GR is local Lorentzian which leads to the local validity of the causality principle, it admits solutions with CTCs. In GR it is known that there are other solutions to the field equations that lead to the violation of causality [1]}, [2]}, [3]}. Here, the gravity is governed by the \(f(R,T)\)  gravity theory, constructed in the Palatini approach. Then various issues must be reexamined in its framework, including the question of whether this gravity theory permits the violation of causality, which is permitted in general relativity. In this paper, the Gödel solution is considered. This cosmological solution of GR has been proposed by K. Gödel [1]}. It is an exact solution of GR with cosmological constant \(\Lambda \)  which leads to the possibility of CTCs, which allow violation of causality.
